A topic that is often hotly debated is how to treat category pages in Joomla from an SEO perspective. You can find many forum topics about this issue and quite often you will see the advice to set these pages to a NOINDEX status. While in some cases this could be the correct way (I sometimes do), I generally advise you not to do so.
In case you don't know what NOINDEX means, check my article about the robots metatag. In short, setting a page to a Noindex status means that you request Google not to index this page. This can be good for pages that add no value themselves from a search engine perspective. Typical examples where this is the case are pages like login-pages or a page where you can reset your password. While of course, these pages are very useful, they don't add valuable content for which you will be found in Google. Setting pages like these to a NOINDEX status makes the other pages stand out and prevents diluted content in Google.
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In the case of category pages, this could also be the case. Look at the following example of a page with a list of articles:
In a case like this, you could argue that the category page in itself does not add any added value: it has no content of itself, just some links to the actual articles. For this reason, it could therefore have a Noindex tag (actually, Noindex, Follow, since the links on the page are useful and should be followed). Still, I usually would probably leave it to the default of Index, Follow, but then still, this is not a page that will usually have high rankings in Google.
Category pages are good candidates for high rankings!
One thing that you should remember is that Category pages are usually high in the link-pyramid that a website usually is. Typically, the homepage is on the top of the pyramid, Category pages one level below and the actual articles create the base of the pyramid:
Pages high up in the pyramid are usually better fit for ranking for broad search terms with high competition while individual articles usually rank for long-tail keywords with low search-volume but high relevancy. The higher the page is in the link-pyramid, the more link-juice it receives from internal links like the main navigation, breadcrumbs and category-references from the individual articles (If link-to-category is active).
If you consider this, it would really be a pity if a page high in the link-pyramid would not be properly optimized. The example with the category-list is indeed an example of a page that is not well-optimized and therefore, it will probably not rank-well, even though it is high in the link-pyramid!
Make sure you optimize these category pages
Optimizing a category page is very easy: make sure to add a heading and add some text: just set the Category-tile to Show and also add a Category-description that you set to Show. You don't need 500 words, but even a little bit of text could make the page stand out a lot more. Also, link to the category from your menu so that it has a nice URL and finally add a proper page-titloe and meta description (of course).
If you do this properly, your Category pages could really work well. If you look at my site, it ranks pretty good on the search term "joomla seo". However, you see that it also has a few sitelinks that correspond to my category pages for the SEO Checklist and the Performance category:
Those pages contain links to the underlying articles, but they also have their own, unique text. Imagine what would have happened if I had set these pages to a Noindex status.... Not a good idea.
Writing a proper category description is not always easy, but is very important. You can use it to rank specifically for broad terms. Imagine if you have a webshop for pets. You will probably offer many kinds of dog-food. While the individual articles are written specifically for the food (brand, individual characteristics), you could write a specific text for the category dog-food. You could write about how to choose a type of dog-food or maybe even show a tool that helps customers decide. This page could really rank well and once on your site, customers will easily navigate to their dog-food of choice.
And what about tags?
Note that the same pretty much counts for tag-pages. If you use tags, best is to ensure each tag-page is unique and valuable with its own content. Best is also not to have too many tag-pages.
If you really have a lot of tags (which I often see), this may indeed lead to too many empty tag-pages and if this is the case, it could still be a good idea to set those pages to Noindex, Follow.